It is, of course, generally known to engrave products with text, numbers, designs, and the like. Engraving usually involves incising characters onto a hard, flat surface by cutting grooves therein. Engraving has multiple uses including individual use and commercial reproduction. Although modern technological advances in photography and printing have almost completely replaced any commercial reproductive use of engraving, individual engraving still exists today. Individual engraving is commonly used in multiple industries including glass, gem, jewelry, gun, metal, and plastic industries. It is often used to insert serial number or other identifying features into otherwise inseparable products or goods.
Generally, engraving may be done with hand tools, with mechanical tools, or with intricate and advanced machines. Tools, such as gravers or burins, have been used for centuries and come in many forms including, without limitation, angled graver, ring graver, round graver, square graver, knife graver, flat graver, v-point graver, mezzotint rockers, roulettes and burnishing tool.
Mechanical tools, such as a pantograph, may be utilized to enlarge, copy, or shrink an engraving. Specifically, a pantograph is a mechanical linkage with a parallelogram connection that produces movements in one location that are identical to movements in another location. The spacing of a pantograph may determine whether an engraving is enlarged, identical, or miniaturized. Tools such as this may be used in combination with hand tools to further enhance hand engraving.
Engraving machines may utilize all of the above tools in combination with a computer to engrave a product. Other engraving machines may use diamond styluses, lasers, or other engraving means to replicate the aforementioned tools. Often, a computer-aided machine engraving machine utilizes three-dimension Cartesian coordinate systems to replicate the angles, depth, and other distinct engravings that hand tools would otherwise provide.
No matter which type of engraving process one uses, mathematics is commonly involved to precisely design the engraving. Specifically, geometry is often used to determine spatial placement of characters, images, and the like. More commonly, vectors, curves, lines, sinusoids, and other complex formulas and functions are used to define and create the engraving. These complex formulas and functions often require knowing the starting point, starting angle, end point, ending angle, coordinates, other angles, radiuses, perimeters, centers, heights, lengths, circumferences, or the like to design the engraving. However, it is common that some or all of these factors are unknown at the time of engraving. A need exists for apparatuses, systems, and methods for estimating the geometry involved with engraving without knowledge of specific factors.
Commonly, someone utilizes these complex formulas and functions to design blueprints for engraving. While blueprints provide a plan for engraving an item or product, they also require precise interpretation and/or measurements by another party before the engraving process may begin. This requires that the interpreter of the blueprint have the skills to understand and comprehend the complex formulas and functions embedded therein. Often, machine operators are not trained to interpret blueprints and lack the necessary skills in order to utilize them properly. Even more frequently, blueprints may not even be available for a particular engraving and therefore the design must be done from scratch. A need, therefore, exists for apparatuses, systems, and methods that do not require advanced training or blueprints.
Additionally, these complex formulas and functions (whether or not they are described in a blueprint) must be programmed into a computer-aided machine engraving machine in order for it to precisely engrave according to the complex formula or function. However, much like the variables the help define the complex formulas and functions, each complex formula or function can vary according to what is needed. A first complex formula or function defining a first shape with a first size in a first location will not be the same as a second complex formula or function defining a second shape with a second size in a second location. Precisely defining each individual complex formula or function in order to engrave an object can become tedious and time consuming. Not only does work need to be performed to define each specific complex formula or function, but work also needs to be performed to enter these specific complex formula or functions into the computer-aided machine engraving machine. This two-step redundancy is not only tedious and time consuming, but it also increases the likelihood for transcription errors. A need, therefore, exists for apparatuses, systems, and methods for estimating specific complex formulas or functions based on a plurality of points and engraving based on said estimation.